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Gonit Puja | গণিত পূজা
Q10. Let f(x) = x² on the interval [1, 3]. The value of c satisfying Lagrange’s Mean Value Theorem is:
(A) 1
(B) 2
(C) 3
(D) 4
1 week ago | [YT] | 0
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Gonit Puja | গণিত পূজা
Q9. The Bolzano–Weierstrass theorem states that:
(A) Every bounded sequence in R has a convergent subsequence
(B) Every unbounded sequence in R is convergent
(C) Every convergent sequence is unbounded
(D) Every sequence in R is monotonic
1 week ago | [YT] | 0
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Gonit Puja | গণিত পূজা
Q8. Which of the following sets is countable?
(A) The set of all real numbers
(B) The set of irrational numbers in (0, 1)
(C) The set of integers Z
(D) The interval (0, 1)
1 week ago | [YT] | 0
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Gonit Puja | গণিত পূজা
Q7. According to the Heine–Borel theorem, a subset of R is compact if and only if it is:
(A) Open and bounded
(B) Closed and bounded
(C) Open and closed
(D) Closed and unbounded
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Gonit Puja | গণিত পূজা
Q6. Which of the following statements is true?
(A) Every continuous function on an open interval is uniformly continuous
(B) Every differentiable function on R is bounded
(C) Every continuous function on a compact interval [a, b] is uniformly continuous
(D) Every bounded function is continuous
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Gonit Puja | গণিত পূজা
Q5. Consider the function f(x) = |x| on R. At x = 0, the function is:
(A) Continuous and differentiable
(B) Continuous but not differentiable
(C) Discontinuous but differentiable
(D) Neither continuous nor differentiable
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Gonit Puja | গণিত পূজা
Q4. The series
Σₙ₌₁∞ (−1)ⁿ⁺¹/n
is:
(A) Absolutely convergent
(B) Conditionally convergent
(C) Divergent
(D) A finite sum
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Gonit Puja | গণিত পূজা
Q3. The sequence aₙ = (−1)ⁿ/n has the limit:
(A) 1
(B) −1
(C) 0
(D) The sequence is divergent
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Gonit Puja | গণিত পূজা
Q2. Let (aₙ) be a monotonically increasing sequence of real numbers that is bounded above. Then:
(A) (aₙ) is divergent
(B) (aₙ) is convergent
(C) (aₙ) is necessarily periodic
(D) (aₙ) is unbounded
1 week ago | [YT] | 0
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Gonit Puja | গণিত পূজা
Q1. Evaluate the following limit:
lim(n→∞) [√(n² + 4n) − n]
(A) 1
(B) 2
(C) 4
(D) 0
1 week ago | [YT] | 0
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